Exam 9: Introduction to Hypothesis Testing

A company that sells an online course aimed at helping high-school students improve their SAT scores has claimed that SAT scores will improve by more than 90 points on average if students successfully complete the course.To test this,a national school counseling organization plans to select a random sample of n = 100 students who have previously taken the SAT test.These students will take the company's course and then retake the SAT test.Assuming that the population standard deviation for improvement in test scores is thought to be 30 points and the level of significance for the hypothesis test is 0.05,what is the probability that the counseling organization will incorrectly "accept" the null hypothesis when,in fact,the true mean increase is actually 95 points?

When testing a hypothesis involving population proportions,an increase in sample size will result in a smaller chance of making a Type I statistical error.

If the hypothesis test you are conducting is a two-tailed test,which of the following is a possible step that you could take to increase the power of the test?

If the p value is less than α in a two-tailed test,

A two-tailed hypothesis test is used when the null hypothesis looks like the following: H_o : = 100.

Type II error is failing to reject the null hypothesis when the null is actually false.

The reason for using the t-distribution in a hypothesis test about the population mean is:

Explain what is meant by a p-value.

The R.D.Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice.When the machine is running properly,the average number of fluid ounces in the cup should be 14.Periodically the machines need to be tested to make sure that they have not gone out of adjustment.To do this,six cups are filled by the machine and a technician carefully measures the volume in each cup.In one such test,the following data were observed: observed: Based on these sample data,which of the following is true if the significance level is .05?

What is meant by the terms Type I and Type II statistical error?

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces.The standard deviation is known to be 0.20 ounces.Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles,which of the following would be the upper tail critical value?

After completing sales training for a large company,it is expected that the salesperson will generate a sale on at least 15 percent of the calls he or she makes.To make sure that the sales training process is working,a random sample of n = 400 sales calls made by sales representatives who have completed the training have been selected and the null hypothesis is to be tested at 0.05 alpha level.Suppose that a sale is made on 36 of the calls.Based on these sample data,which of the following is true?

The chance of making a Type II statistical error increases if the "true" population mean is closer to the hypothesized population mean,all other factors held constant.

A company makes a device that can be fitted to automobile engines to improve the mileage.The company claims that if the device is installed,owners will observe a mean increase of more than 3.0 mpg.Assuming that the population standard deviation of increase is known to be 0.75 mpg,and a sample of size 64 cars is selected,what is the probability of "accepting" the null hypothesis if the true population mean is 3.10 mpg increase? Assume that the test will be performed using a 0.05 level of significance.

The director of the city Park and Recreation Department claims that the mean distance people travel to the city's greenbelt is more than 5.0 miles.Assuming that the population standard deviation is known to be 1.2 miles and the significance level to be used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed,the probability of a Type II error is approximately .4545 when the "true" population mean is 5.5 miles.

A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars.It is believed that the population standard deviation is 3 mpg.Based upon this information,if the "true" population mean is 32.0 mpg,what is the probability that the test will lead the consumer group to reject the claimed mileage for this car?

Woof Chow Dog Food Company believes that it has a market share of 25 percent.It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food.The appropriate null and alternate hypotheses are:

The director of the city Park and Recreation Department claims that the mean distance people travel to the city's greenbelt is more than 5.0 miles.Assuming that the population standard deviation is known to be 1.2 miles and the significance level to be used to test the hypothesis is 0.05 when a sample size of n = 64 people are surveyed,the critical value is approximately 4.75 miles.

If the sample data lead the decision maker to reject the null hypothesis,the alpha level is the maximum probability of committing a Type II error.

The Gordon Beverage Company bottles soft drinks using an automatic filling machine.When the process is running properly,the mean fill is 12 ounces per can.The machine has a known standard deviation of 0.20 ounces.Each day,the company selects a random sample of 36 cans and measures the volume in each can.They then test to determine whether the filling process is working properly.The test is conducted using a 0.05 significance level.Using the test statistic approach,what conclusion should the company reach if the sample mean is 12.02 ounces? What type of statistical error may have been committed?